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16 Sep 2014, 00:55

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55% (hard)

Question Stats:

62%(03:01) correct 38%(03:05) wrong based on 42 sessions

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A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). If the weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver, what will be the weight of a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum?

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16 Sep 2014, 00:55

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Official Solution:

A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). If the weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver, what will be the weight of a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum?

A. 36 gramsB. 40 gramsC. 42 gramsD. 48 gramsE. 50 grams

Denote \(S\) as the weight of silver and \(A\) the weight of aluminum in the first coin. Compose the following equation: \(S + A = 30\) or \(2A + A = 30\). Thus, the aluminum half of the coin weighs 10 grams. If the coin were made of pure aluminum, the second half of the coin would also weigh 10 grams and the whole coin would weigh 20 grams.

If we look at the proportions of the second coin, we will see that it is twice as large as the first coin (volume2 = \((\frac{30}{2})^2*\pi\); volume1 = \(2*(\frac{15}{2})^2*\pi\)). A second coin made of pure aluminum would be twice as heavy as the first coin made of pure aluminum. The answer to the question is therefore \(20*2 = 40\) grams.

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06 Dec 2015, 11:34

Dear Bunuel,

Please explain sentence "second coin made of pure aluminum would be twice as heavy as the first coin made of pure aluminum"? Unfortunately, I don't understand your logic on deriving 20gram (second coin is composed of A only and we dont know how many A in there) and then multiplying it by 2.

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07 Dec 2015, 08:16

Liza99 wrote:

Dear Bunuel,

Please explain sentence "second coin made of pure aluminum would be twice as heavy as the first coin made of pure aluminum"? Unfortunately, I don't understand your logic on deriving 20gram (second coin is composed of A only and we dont know how many A in there) and then multiplying it by 2.